Isometric immersions of higher codimension into the product {mathbf S^k times H^(n+p-k)} of sphere and hyperboloid

In this paper, we obtain a sufficient and necessary condition for a simply connected Riemannian manifold $(M^n, g)$ to be isometrically immersed, as a submanifold with codimension $p\geq 1$, into the product $S^k\times H^{n+p-k}$ of sphere and hyperboloid.